Wireless channels are characterized by complex physical layer effects resulting from multiple users sharing spectrum in a multipath fading environment. In such environments, reliable communication is sometimes possible only through the use of diversity techniques in which the receiver processes multiple replicas of the transmitted signal under varying channel conditions. Antenna diversity techniques have received considerable attention recently due to the significant gains promised by information-theoretic studies. While the use of multiple receive antennas is a well-explored problem, the design of space-time (ST) signals that exploit the available capacity in multi-transmit antenna or multi-transmit/multi-receive antenna systems still faces many challenges. Tarokh et al. coined the name space-time coding for this two-dimensional signal design paradigm. Over the past five years, several ST coding schemes have been proposed in the literature.
The design of full diversity algebraic constellations for the Rayleigh-fading channel was pioneered by Boullé and Belfiore. The main idea behind their work is to introduce redundancy in the signal space (or signal space diversity) when the signal constellation is carved from some algebraic lattices. Signal space diversity can be obtained by applying fully diverse unitary transformations to inputs drawn from lattices or multidimensional digital modulation signals carved from a number ring, such as pulse amplitude modulation (PAM) or quadrature amplitude modulation (QAM) constellations. The resulting constellations have the property that each point is uniquely determined by any of its components which allows for the possibility of retrieving the whole point if some of the components are lost in a deep fade.